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Discovering the forbidden Raman modes at the edges of layered materials

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Science Advances  14 Dec 2018:
Vol. 4, no. 12, eaau6252
DOI: 10.1126/sciadv.aau6252
  • Fig. 1 Raman spectroscopy of MoS2.

    (A) Schematic illustration of Raman backscattering spectroscopy. (B) Raman-active modes of 2H-phase TMDCs in the high frequency range. (C) Raman spectra of MoS2 from the edge and from the body region. a.u., arbitrary units. (D) Optical image of a specific MoS2 flake with the orthogonal armchair and zigzag edges. The intensity of E1g signal is shown in (E) for [ei, es] = [X, X], (F) for [ei, es] = [Y, Y], (G) for [ei, es] = [X, Y], and (H) for [ei, es] = [Y, X]. The white arrows in (E) to (H) indicate the positions of the edges, corresponding to the black one-way arrows in (D).

  • Fig. 2 Raman spectra of WS2 and WSe2.

    (A to C) Raman spectra of WS2 from (A) the body region, (B) the armchair edge, and (C) the zigzag edge. (D to F) Raman spectra of WSe2 from (D) the body region, (E) the armchair edge, and (F) the zigzag edge. The spectra vary with the polarization direction of the incident light ei and the scattered Raman signal es (X or Y).

  • Fig. 3 Raman shift ratio of the E1g and E2g as a function of the atomic mass ratio in 2H-phase TMDCs.
  • Fig. 4 Raman spectroscopy of BP.

    (A) Atomic structure and image of a BP flake with the orthogonal armchair edge and the zigzag edge. (B) Raman-active modes of BP in the high frequency range. (C to E) Raman spectra of BP from (C) the body region, (D) the armchair edge, and (E) the zigzag edge. The spectra vary with the polarization directions (X or Y) of the incident light ei and the scattered Raman signal es.

  • Fig. 5 Electric field of the incident light and the scattered Raman signal at the edge of a MoS2 flake.

    The cross-profile is in the xz plane, with the edge direction along y. (A) The incident light from the z direction is polarized in the x direction with ei = (1, 0, 0). (B) The incident light from the z direction is polarized in y direction with ei = (0, 1, 0). The electric field amplitude is shown in (A) and (B). (C) Scattered Raman light with original polarization along z, a portion of the light propagates in the z direction with its polarization direction in x.

  • Table 1 Calculated expression of Iedge for the forbidden Raman modes.

    Correspondingly, a “yes” indicates that the mode is experimentally detected, while a “no” indicates that the mode is not experimentally detected. N/A, not applicable.

    E1g mode of MoS2,
    WS2, and WSe2
    [ei, es]
    [X, X][Y, Y][X, Y][Y, X]
    Armchair (X)Iedge0d2iz2δsy2 + δiy2δsz2)d2δsz2d2δiz2
    DetectedNoYesYesYes
    Zigzag (Y)Iedged2iz2δsx2 + δix2δsz2)0d2δiz2d2δsz2
    DetectedYesNoYesYes
    B1g of BP[ei, es]
    [X, X][Y, Y][X, Y][Y, X]
    Armchair (X)Iedge0h2iz2δsy2 + δiy2δsz2)00
    DetectedNoYesNoNo
    Zigzag (Y)Iedge00h2δiz2h2δsz2
    DetectedYes (weak)NoYesYes
    B13g of BP[ei, es]
    [X, X][Y, Y][X, Y][Y, X]
    Armchair (X)Iedge00i2δsz2i2δiz2
    DetectedNo0YesYes
    Zigzag (Y)Iedgei2iz2δsx2 + δix2δsz2)000
    DetectedYesNoNoNo
    B23g of BP[ei, es]
    [X, X][Y, Y][X, Y][Y, X]
    Armchair (X)Iedge00j2δsz2j2δiz2
    DetectedNoNoN/AN/A
    Zigzag (Y)Iedgej2iz2δsx2 + δix2δsz2)000
    DetectedYesNoN/AN/A

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaau6252/DC1

    Section S1. Raman tensors of MoS2, WS2, WSe2, BP, and PtS2 (high frequency range)

    Section S2. Scattering of the E1g mode from the body region

    Section S3. Intensity maps of the MoS2, E2g, and A1g peaks

    Section S4. Raman spectra of MoS2 from the body region, the armchair edge, and the zigzag edge

    Section S5. Raman modes and spectra of PtS2

    Section S6. Analysis on the edge phonons

    Section S7. Calculation of Iedge = |eiedge·R·esedge|2

    Section S8. Quantitative computation of Iedge

    Section S9. Raman spectra in other types of edge sites

    Section S10. Raman spectra from the MoS2 powder and dispersion samples

    Table S1. Raman tensors and intensity expressions of layered materials at high frequency range.

    Fig. S1. Cross-sectional image of the electromagnetic field of the E1g Raman signal.

    Fig. S2. Intensity maps of the MoS2 E2g, and A1g peaks.

    Fig. S3. Raman spectra of MoS2.

    Fig. S4. Raman spectra of PtS2.

    Fig. S5. Simulated edge phonon modes in the range of 260 to 300 cm−1.

    Fig. S6. Computation of the forbidden Raman mode intensity at the edge region.

    Fig. S7. Electric field component of incident light and scattered Raman signal at the edge site of polycrystalline BP.

    Fig. S8. Incident light, scattered Raman light, and Raman spectra from edge sites where thickness changes.

    Fig. S9. Raman spectra from powder and dispersion samples.

    References (3440)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Raman tensors of MoS2, WS2, WSe2, BP, and PtS2 (high frequency range)
    • Section S2. Scattering of the E1g mode from the body region
    • Section S3. Intensity maps of the MoS2, E2g, and A1g peaks
    • Section S4. Raman spectra of MoS2 from the body region, the armchair edge, and the zigzag edge
    • Section S5. Raman modes and spectra of PtS2
    • Section S6. Analysis on the edge phonons
    • Section S7. Calculation of Iedge = |eiedge·R·esedge|2
    • Section S8. Quantitative computation of Iedge
    • Section S9. Raman spectra in other types of edge sites
    • Section S10. Raman spectra from the MoS2 powder and dispersion samples
    • Table S1. Raman tensors and intensity expressions of layered materials at high frequency range.
    • Fig. S1. Cross-sectional image of the electromagnetic field of the E1g Raman signal.
    • Fig. S2. Intensity maps of the MoS2 E2g, and A1g peaks.
    • Fig. S3. Raman spectra of MoS2.
    • Fig. S4. Raman spectra of PtS2.
    • Fig. S5. Simulated edge phonon modes in the range of 260 to 300 cm−1.
    • Fig. S6. Computation of the forbidden Raman mode intensity at the edge region.
    • Fig. S7. Electric field component of incident light and scattered Raman signal at the edge site of polycrystalline BP.
    • Fig. S8. Incident light, scattered Raman light, and Raman spectra from edge sites where thickness changes.
    • Fig. S9. Raman spectra from powder and dispersion samples.
    • References (3440)

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